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What do you mean if εo isn't constant? Do you mean for cases where there is matter between the surface and the charge, and thus you need to account for a drop in the E field due to the permittivity of that matter? |
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What do you mean if εo isn't constant? Do you mean for cases where there is matter between the surface and the charge, and thus you need to account for a drop in the E field due to the permittivity of that matter? --BlackGriffen |
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::Upon further reflection, that is wrong. The dielectric constant of matter doesn't just magically reduce the electric field. The dielectric constant (I had the wrong name previously) is a measure of how easy it is to separate the molecules of matter in to a dipole. To show why is relatively easy (now that I think about it properly). Consider a small positively charged sphere. The electric field outside this sphere is is the same is if it was a point charge: kq/r2. Stick a neutrally charged spherical shell around it. The electric field of the sphere creates dipoles within the shell that surrounds it. The net effect is like two thin shells of charge have formed; a negative one on the inner surface of the shell and a positive one on the outer surface. The charges of these shells have to be precisely equal due to conservation of charge. The net effect? Everywhere but on the inside of the walls of the neutral shell, the electric field still looks like kq/r2. Within the walls of the shell the electric field is weaker, but as long as the surface entering that region removes no net charge, the decrease in the electric field is compensated for by two factors: a change in the area of integration, the fact that the charge shells are approximations of microscopic dipoles means that there is still a net surface charge that compensates for the inner charge. Even in the limiting case, metals, where the surface charges are great enough to reduce the electric field in the body of the metal to zero, Gauss's law holds. --BlackGriffen |
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I deliberately left the history empty because I did not know it. I do know that the wave equations for light that can be derived from them led to relativity. (the term describing the velocity of the wave was 1/(μoεo).5 which is equal to c, and the fact that it didn't contain a term for the velocity of the observer is what sparked Einstein's imagination/lead to his postulate that c is a constant to any observer. |
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I deliberately left the history empty because I did not know it. By all means, add a history section. I do know that the wave equations for light that can be derived from them led to relativity. (the term describing the velocity of the wave was 1/(μoεo).5 which is equal to c, and the fact that it didn't contain a term for the velocity of the observer is what sparked Einstein's imagination/lead to his postulate that c is a constant to any observer. |
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Also, 4 Maxwell's equations with 4 variables (time, charge density, the electric field, and the magnetic field). Where do you get two? |
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Also, 4 Maxwell's equations with 4 variables (time, charge density, the electric field, and the magnetic field). Where do you get two? --BlackGriffen |
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--Initial Author |
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--BlackGriffen |
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--Initial Author |
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--BlackGriffen |
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--Initial Author |
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--BlackGriffen |
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